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Kryger [21]
2 years ago
6

You are making a banner. You have a sheet of paper that is 2 m wide and want to leave a 35-cm blank margin on either side. How m

any centimeters can you use for text?
Mathematics
1 answer:
Dennis_Churaev [7]2 years ago
7 0
<span>100 cm = 1 meter.
Ok you have 200 cm of paper. Each side needs 35 cm for a margin so:
35 + 35 = 70.
Then subtract 70 from 200 and you are left with 130 cm of space left for text.</span>
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Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each
GarryVolchara [31]

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each of the following.

(i)    3 to 4

(ii)    3 to 3.5

(iii)    3 to 3.1

(b) Find the instantaneous rate of change when r = 3.  A'(3)

Area of a circle A(r)= πr²

The average rate of change of the area of a circle with respect to its radius

ΔA(r)/Δr = πr₂²-πr₁²/r₂-r₁

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

i) If the radius changes from 3 to 4

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(4²-3²)/4-3

ΔA(r)/Δr = π(16-9)/1

ΔA(r)/Δr = 7π

<em>Hence, average rate of the area of a circle when the radius changes from 3 to 4 is 7π</em>

ii) If the radius changes from 3 to 3.1

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(3.5²-3²)/3.5-3

ΔA(r)/Δr = π(12.25-9)/0.5

ΔA(r)/Δr = 3.25π/0.5

ΔA(r)/Δr = 6.5π

<em>Hence, average rate of the area of a circle when the radius changes from 3 to 3.5 is </em>6.5π

iii) If the radius changes from 3 to 3.1

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(3.1²-3²)/3.1-3

ΔA(r)/Δr = π(9.61-9)/0.1

ΔA(r)/Δr = 0.61π/0.1

ΔA(r)/Δr = 6.1π

<em>Hence, average rate of the area of a circle when the radius changes from 3 to 3.1 is </em> 6.1π

iv) Instantaneous rate of change A'(r) = 2πr

When r = 3;

A'(3) = 2π(3)

A'(3) = 6π

<em>Hence, the instantaneous rate of change when r = 3 is 6π </em>

5 0
3 years ago
A convex hexagon has interior angles with measures x^0, (5x - 103); (2x + 60), (7x - 31), (6x -6), and (9x - 100), what is the v
cestrela7 [59]

Answer:

x = 30.66°

Step-by-step explanation:

The sum of the interior angles of a hexagon is 720°

Each angles are x^0, (5x - 103); (2x + 60), (7x - 31), (6x -6), and (9x - 100),

we add all these angles together

x^0 + (5x - 103) + (2x + 60) + (7x - 31) + (6x -6) + (9x - 100) = 720

x^0  = 1

1 + (5x - 103) + (2x + 60) + (7x - 31) + (6x -6) + (9x - 100)

1 + 5x - 103 +2x + 60 + 7x -31 + 6x - 6 + 9x - 100 = 720

1 - 103 + 60 - 31 - 6 - 100 + 5x + 2x + 7x + 6x + 9x = 720

1 - 180 + 29x = 720

-179 + 29x = 720

29x = 720 + 179 = 889

x = 889/29 = 30.655 ≅ 30.66°

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Translate the shape A three squares right and three squares up.
aleksandr82 [10.1K]

Based on the graph given, the coordinates of the vertices of the image are (4,4) (6,4) (4,7).

<h3>What is the coordinate about?</h3>

In the graph above, the coordinate given are: (1,1) (3,1) (1,4) To be able to find the coordinates of the vertices, we need to translate 3 square up and also 3 square down and as such it will be:

(x + 3, y + 3)

( 1 + 3, 1 + 3) = (4,4)

( 3 + 3, 1 + 3) = (6,4)

( 1 + 3, 4 + 3) = (4,7).

Therefore, Based on the graph given, the coordinates of the vertices of the image are (4,4) (6,4) (4,7).

Learn more about coordinates from

brainly.com/question/17206319

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ivann1987 [24]

Answer:

$136.8

Step-by-step explanation:

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Step 1: I drew a visual representation

Step 2: write the formulae for the volume of a sphere which is V=4*PI*r cubed all divided by 3. Refer to my image

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3 years ago
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